98 M. Ramond's Instructions for the Application of [Aug. 



This number, in fact, once determined either by observation 

 or experiment, serves for all subsequent operations ; by making 

 the modifications which the difference of circumstances in each 

 case requires : this is what we call the constant coejjicient of the 

 formula. 



Thus, in order to measure the height of a mountain, the fun- 

 damental operation consists in observing the barometer both at 

 the foot and the summit : taking out of the ordinary tables the 

 logarithms corresponding to the oarometric heights expressed in 

 units of the same denomination and decimal parts of those units: 

 subtracting the smaller from the greater logarithm, and multi- 

 plying the difference by the constant coefficient. The product 

 will give the height required in measures of the same denomina- 

 tion as those which entered into the determination of the coeffi- 

 cient : and this height will be correct if we operate under the 

 same circumstances which were supposed in determining the 

 coefficient. 



These circumstances are, as has been observed, a certain 

 atmospheric pressure and a certain temperature, from whence 

 results a certain ratio between the densities of air and mercury. 

 The coefficient supposes them constant : they are in reality very 

 variable ; it must, therefore, undergo certain modifications analo- 

 gous to the changes with which these circumstances may be 

 affected. 



In the formula of M. de Laplace, for example, the coefficient 

 is determined for the level of the sea, the temperature of melting 

 ice, and the latitude 45'^. It is then only accurate for this single 

 case, and the formula would be incomplete and inapphcable to 

 other cases, if it did not comprise corrections suited to the varia- 

 tions of these first data. 



The most important of these corrections relates to the 

 variations of temperature ; it is easy to conceive the principle of 

 this, and to feel its necessity. Heat dilates air: it augments its 

 volume, and diminishes its density. With equal weight, it occu- 

 pies more space ; with equal volume, it has less weight. If we 

 suppose a stratum of air of 1000 feet in thickness mtercepted 

 between the levels of the base and summit of a mountain, this 

 stratum will weigh less at a temperature of 10° centigrade than 

 at zero. The difference of the heights of the barometer observed 

 at the two stations will be less in the former than in the latter 

 case ; and if we apply the same coefficient to the two logarith- 

 mic differences, we shall have two very different measures of one 

 and the same height; the mountain will seem to diminish in 

 height in proportion as the temperature increases. Now the 

 coefficient being calculated for the temperature of melting ice, 

 we must, inconsequence, increase or diminish its value, accord- 

 ingas the temperature rises above, or sinks below, that point. 



Experiment has taught us that the variation of air in volume is 

 nearly 1^167th fur a variation of 1° centigrade : supposing the 



